Recent developments in the field of deep learning have motivated many researchers to apply these methods to problems in quantum information. Torlai and Melko first proposed a decoder for surface codes based on neural networks. Since then, many other researchers have applied neural networks to study a variety of problems in the context of decoding. An important development in this regard was due to Varsamopoulos et at. who proposed a two-step decoder using neural networks. Subsequent work of Maskara et at. used the same concept for decoding for various noise models. We propose a similar two-step neural decoder using inverse parity-check matrix for topological color codes. We show that it outperforms the state-of-the-art performance of non-neural decoders for independent Pauli errors noise model on a 2D hexagonal color code. Our final decoder achieves a threshold of 10%. Our result is comparable to the recent work on neural decoder for quantum error correction by Maskara et at. It appears that our decoder has advantages with respect to training cost and complexity of the network for higher distances when compared to that of Maskara et at.
Recent developments in the field of deep learning have motivated many researchers to apply these methods to problems in quantum information. Torlai and Melko first proposed a decoder for surface codes based on neural networks. Since then, many other researchers have applied neural networks to study a variety of problems in the context of decoding. An important development in this regard was due to Varsamopoulos et at. who proposed a two-step decoder using neural networks. Subsequent work of Maskara et at. used the same concept for decoding for various noise models. We propose a similar two-step neural decoder using inverse parity-check matrix for topological color codes. We show that it outperforms the state-of-the-art performance of non-neural decoders for independent Pauli errors noise model on a 2D hexagonal color code. Our final decoder achieves a threshold of 10%. Our result is comparable to the recent work on neural decoder for quantum error correction by Maskara et at. It appears that our decoder has advantages with respect to training cost and complexity of the network for higher distances when compared to that of Maskara et at.
Finding optimal correction of errors in generic stabilizer codes is a computationally hard problem, even for simple noise models. While this task can be simplified for codes with some structure, such as topological stabilizer codes, developing good and efficient decoders still remains a challenge. In our paper, we systematically study a very versatile class of decoders based on feedforward neural networks. To demonstrate adaptability, we apply neural decoders to the triangular color and toric codes under various noise models with realistic features, such as spatially correlated errors. We report that neural decoders provide a significant improvement over leading efficient decoders in terms of the error-correction threshold. In particular, the neural decoder threshold for the two-dimensional color code is very close to the toric code threshold. Using neural networks simplifies the design of decoders and does not require prior knowledge of the underlying noise.
Solving for quantum error correction remains one of the key challenges of quantum computing. Traditional decoding methods are limited by computing power and data scale, which restrict the decoding efficiency of color codes. There are many decoding methods that have been suggested to solve this problem. Machine learning is considered one of the most suitable solutions for decoding task of color code. We project the color code onto the surface code, use the deep Q network to iteratively train the decoding process of the color code and obtain the relationship between the inversion error rate and the logical error rate of the trained model and the performance of error correction. Our results show that through unsupervised learning, when iterative training is at least 300 times, a self-trained model can improve the error correction accuracy to 96.5%, and the error correction speed is about 13.8% higher than that of the traditional algorithm. We numerically show that our decoding method can achieve a fast prediction speed after training and a better error correction threshold.
Abstract Decoding is the most important part of the error correction process. During thedecoding process, the main idea of this paper is to transfer the error measuredinside ancilla qubit to the boundary, and decompose the error into the productof stabilizer, logical error and pure error, stabilizer error do not affect logicalerror. Therefore, the result of error syndrome is only affected by pure error,while the error of stabilizer can be ignored. Decoding by neural network can takeadvantage of its high threshold and adaptability to training different codes. Thefocus of this work is to propose a suitable algorithm for neural network decodingof planar codes, so as to reduce the size of the neural network as much as possiblewithout compromising the decoding performance. Comparative experiments wereconducted using the minimum weight perfect matching(MWPM) decoder andthe neural network decoder to compare the decoding performance of planar codeswith code distances of 5, 7, and 9, respectively, demonstrating high threshold ofneural network decoder and its adaptability to training different codes. Takingthe planar code with code distance of 5 as an example, the pseudo-thresholdsobtained using the MWPM decoder and the neural network decoder are 0.005and 0.0068 respectively,increased by 36%. It shows that for planar code, theneural network decoder significantly outperforms the MWPM decoder.
Surface codes are a promising method of quantum error correction and the basis of many proposed quantum computation implementations. However, their efficient decoding is still not fully explored. Recently, approaches based on machine learning techniques have been proposed by Torlai and Melko [Phys. Rev. Lett. 119, 030501 (2017)] as well as Varsamopoulos et al. [Quantum Sci. Technol. 3, 015004 (2017)]. In these approaches, a so-called high-level decoder is used to post-correct an underlying decoder by correcting logical errors. A significant problem is that these methods require large amounts of training data even for relatively small code distances. The above-mentioned methods were tested on the rotated surface code which encodes one logical qubit. Here, we show that they are viable even for the toric surface code which encodes two logical qubits. Furthermore, we explain how symmetries of the toric code can be exploited to reduce the amount of training data that is required to obtain good decoding results. Finally, we compare different underlying decoders and show that the accuracy of high-level decoding noticeably depends on the quality of the underlying decoder in the realistic case of imperfect training.
A quantum computer needs the assistance of a classical algorithm to detect and identify errors that affect encoded quantum information. At this interface of classical and quantum computing the technique of machine learning has appeared as a way to tailor such an algorithm to the specific error processes of an experiment—without the need for a priori knowledge of the error model. Here, we apply this technique to topological color codes. We demonstrate that a recurrent neural network with long short-term memory cells can be trained to reduce the error rate L of the encoded logical qubit to values much below the error rate phys of the physical qubits—fitting the expected power law scaling , with d the code distance. The neural network incorporates the information from 'flag qubits' to avoid reduction in the effective code distance caused by the circuit. As a test, we apply the neural network decoder to a density-matrix based simulation of a superconducting quantum computer, demonstrating that the logical qubit has a longer life-time than the constituting physical qubits with near-term experimental parameters.
Fault-tolerant quantum computing will require error rates far below those achievable with physical qubits. Quantum error correction (QEC) bridges this gap, but depends on decoders being simultaneously fast, accurate, and scalable. This combination of requirements remains unmet by a machine-learning decoder, nor by any decoder for promising resource-efficient codes such as the color code. Here we introduce AlphaQubit 2, a neural-network decoder that achieves near-optimal logical error rates for both surface and color codes at scale under realistic noise. For the color code, it is orders of magnitude faster than other high-accuracy decoders. We demonstrate real-time decoding faster than 1μs per cycle on commercial accelerators: for the surface code to distance 11, with better accuracy than leading real-time decoders; and the first real-time decoding of the color code to distance 9. These results support the practical application of a wider class of promising QEC codes, and establish a credible path towards high-accuracy, real-time neural decoding at the scales required for fault-tolerant quantum computation.